The primary objectives of this study are to determine the safety and immunogenicity of varicella vaccine in HIV-infected children. In the first phase of this study, only children who were varicella-naove and asymptomatic or mildly symptomatic were enrolled. In addition, children had to have normal CD4 cell counts. Enrollment into this phase of the study has been completed. Based on results obtained (see below), the protocol was amended to allow enrollment of a second cohort of HIV-infected children who have more advanced disease or lower CD4 cell counts, or both. In addition, children who had prior advanced disease and very low CD4 cell counts who developed normal CD4 cell counts after receiving highly active antiretroviral therapy will be enrolled. In addition to parameters of safety, humoral and cell-mediated responses to varicella vaccine are monitored.